Costs: one table, every curve
導入済み| English | 意味 |
|---|---|
| marginal product/ˈmɑːdʒɪnl ˈprɒdʌkt/ | marginal product |
| diminishing returns/dɪˈmɪnɪʃɪŋ rɪˈtɜːnz/ | diminishing returns |
| marginal cost/ˈmɑːdʒɪnl kɒst/ | The additional total cost of producing one more unit of output. |
| fixed cost/fɪkst kɒst/ | A cost that does not change with output within a specified period and relevant range of activity. |
| variable cost/ˈveərɪəbl kɒst/ | A cost whose total changes with the level of output or activity. |
| average total cost/ˈævrɪdʒ ˈtəʊtl kɒst/ | average total cost |
| economies of scale/ɪˈkɒnəmiz ɒv skeɪl/ | Falls in average production cost as the scale of output increases. |
Where a supply decision really comes from
- Nimbus's ovens cost £200 a day whether they bake one loaf or six hundred. Each baker is paid £90. The tenth loaf of the day costs almost nothing; the 550th costs a fortune.
- This lesson derives every cost curve in the textbook from one verified table of bakers and loaves — no accounting spreadsheet required.
Production first: the marginal product
- The shop is small, so as it fills, each extra baker adds less than the one before. With 1 to 10 bakers the daily loaves are 100, 190, 270, 340, 400, 450, 490, 520, 540, 550.
- The marginal product 边际产量 of successive bakers is 100, 90, 80, 70, 60, 50, 40, 30, 20, 10 — diminishing returns 边际报酬递减, the physical law under every rising marginal cost curve.
Output goes from 340 loaves with 4 bakers to 400 with 5. What is the fifth baker's marginal product, in loaves?
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$400 - 340 = 60$ loaves — and the sequence 100, 90, 80, 70, 60… is diminishing returns in numbers.
Costs from production
- Fixed cost 固定成本 is the oven's £200: it does not move with output. Variable cost 可变成本 is the wage bill $90L$, which does.
- The marginal cost 边际成本 of a loaf is the wage divided by what the last baker added: $MC = 90/MPL$. The fifth baker adds 60 loaves, so those loaves cost $90/60 = £1.50$ each.
Fixed, variable or marginal?
Sort the bakery's daily costs. Fixed costs ignore the day's output; variable costs move with it; marginal costs price one more loaf.
The fifth baker is paid £90 and adds 60 loaves. What is the marginal cost of those loaves, in £ per loaf?
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$MC = w/MPL = 90/60 = £1.50$. When MPL falls, the same wage is spread over fewer loaves: MC must rise.
With 8 bakers the bakery makes 520 loaves at a wage bill of £720 plus £200 fixed. What is average total cost, in £ to two decimals?
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$ATC = (720 + 200)/520 = 920/520 = £1.77$ per loaf.
Match each measure to its formula.
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Every cost curve in the unit is one of these four rules applied to the same ten-row table.
The table, verified
| L | Q | MPL | MC | AVC | ATC |
|---|---|---|---|---|---|
| 1 | 100 | 100 | £0.90 | £0.90 | £2.90 |
| 3 | 270 | 80 | £1.13 | £1.00 | £1.74 |
| 5 | 400 | 60 | £1.50 | £1.13 | £1.63 |
| 8 | 520 | 30 | £3.00 | £1.38 | £1.77 |
| 9 | 540 | 20 | £4.50 | £1.50 | £1.87 |
Every column derives from the two before it: $AVC = 90L/Q$ and $ATC = (90L + 200)/Q$. The full ten-row table reproduces exactly these rules.
Three curves, one family
- Plot MC, AVC and ATC from the table: MC rises because MPL falls; the averages sag before it and follow it up.
- Average total cost 平均总成本 bottoms at about £1.63 near Q = 400 — and MC passes through exactly that minimum. When the marginal loaf costs less than the average, the average falls; the grade-point-average logic, priced in bread.
MC passes through ATC's minimum. Why?
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The grade-point-average logic: one small grade pulls the average down, one large one pushes it up. The average can only turn at the marginal value.
The ninth baker, priced
- At the market price of £4 (lesson 0302), the eighth baker's 30 loaves earn $30 \times 4 = £120$ against a £90 wage — worth it. The ninth adds 20 loaves: $20 \times 4 = £80$ against £90 — not worth it.
- So Nimbus runs eight bakers, 520 loaves, profit $4 \times 520 - (90 \times 8 + 200) = £1{,}160$. "Produce while $P \ge MC$" and "hire while the baker's value exceeds the wage" are the same sentence.
The ninth baker adds 20 loaves at £4 each. Should Nimbus hire him?
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The marginal test compares his value (£80) with his cost (£90). Averages and fixed cost do not enter it; his MC is £4.50 against a £4 price.
The shutdown question
- A price war drops the loaf to £0.85 — below even the first baker's £0.90 average variable cost. No scale of baking pays its own wages: shut the ovens, lose the £200 fixed cost, reopen when the price recovers.
- The boundary flips fast: at £1.00, the first 190 loaves cover £180 of wages plus £10 of rent — bake with two bakers and lose £190, not £200. Produce when $P \ge \min AVC$; shut below it.
The price falls to £0.85 a loaf. The smallest average variable cost on the table is £0.90. What should Nimbus do?
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Below minimum AVC no scale even pays the bakers. One baker would bring £85 of revenue against £90 of wages — shut and lose £200, not more.
Nimbus's falling ATC between 100 and 400 loaves shows economies of scale.
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The shop never changed size — that fall is the £200 fixed cost spreading over more loaves, a short-run effect. Scale economies are about changing the shop itself.
Three cost slips
- Reading scale economies from falling ATC. The shop never changed size — that fall is a fixed cost spreading. Economies of scale 规模经济 are long-run.
- Computing MC from a change in ATC. MC is $w/MPL$, straight from production.
- Treating fixed cost as "irrelevant". It is irrelevant to the marginal choice and decisive for the shutdown choice.
Recap
- $MC = w/MPL$; diminishing returns make it rise.
- MC cuts ATC at ATC's minimum; averages chase the marginal.
- Produce while $P \ge MC$; shut down below minimum AVC.